document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102885>Question 102885</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am thinking of three consecutive positive numbers.  If I multiply the first with the third and then add the second, the result is 41.  Let X be the smallest number.  <BR>\n" );
document.write( "This is how far I have made, but I don't think I'm doing it right.<BR>\n" );
document.write( "x <BR>\n" );
document.write( "x+1<BR>\n" );
document.write( "x+2<BR>\n" );
document.write( "x+x+1+x+2=41<BR>\n" );
document.write( "     3x+3=41<BR>\n" );
document.write( "   3x+3-3=41-3<BR>\n" );
document.write( "       3x=38<BR>\n" );
document.write( "   x=38/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74835 by </B><A HREF=/tutors/aboutme.mpl?userid=doukungfoo><B>doukungfoo(195)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=doukungfoo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=doukungfoo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=74835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This part of what you did is correct:<BR>\n" );
document.write( "x<BR>\n" );
document.write( "x+1<BR>\n" );
document.write( "x+2<BR>\n" );
document.write( "This is where you made a mistake:<BR>\n" );
document.write( "x+x+1+x+2=41<BR>\n" );
document.write( "The problem states:<BR>\n" );
document.write( "If I multiply the first with the third and then add the second, the result is 41<BR>\n" );
document.write( "So your equation should look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B2%29%2B%28x%2B1%29=41 ALIGN=MIDDLE  ALT=\"x%28x%2B2%29%2B%28x%2B1%29=41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "first multiply x across (x+2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B%28x%2B1%29=41 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B%28x%2B1%29=41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "next multiply 1 across (x+1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2Bx%2B1=41 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2Bx%2B1=41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x%2B1=41 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x%2B1=41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now move 41 over by subtracting it from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x%2B1-41=41-41 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x%2B1-41=41-41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x-40=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK so now we have a quadratic equation in standard form. We can solve for x by factoring or by using the quadratic formula.<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B3x%2B-40+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B-40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%283%29%5E2-4%2A1%2A-40=169 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A1%2A-40=169\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=169 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C1+=+-8 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C1+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B3x%2B-40 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B3x%2B-40+=+1%28x-5%29%2A%28x--8%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B-40+=+1%28x-5%29%2A%28x--8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 5, -8.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-40+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-40+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "So the possible solutions for x are -8 and 5<BR>\n" );
document.write( "However the problem states:<BR>\n" );
document.write( "I am thinking of three consecutive positive numbers.<BR>\n" );
document.write( "So we can throw out -8 as an extraneous solution.<BR>\n" );
document.write( "Ok so the smallest number is 5<BR>\n" );
document.write( "the next number is 5+1 which is 6<BR>\n" );
document.write( "and the last number is 5+2 which is 7<BR>\n" );
document.write( "<b>Answer: The three consecutive positive numbers are 5, 6, and 7</b><BR>\n" );
document.write( "Check by mulitiplying the first number by the third number and adding the second number. The result should be 41.<BR>\n" );
document.write( "5 * 7 + 6 = 41<BR>\n" );
document.write( "35 + 6 = 41<BR>\n" );
document.write( "41 = 41<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );